LINEAR APPROXIMATION METHODS AND THE BEST APPROXIMATIONS OF THE POISSON INTEGRALS OF FUNCTIONS FROM THE CLASSES H_(ωp) IN THE METRICS OF THE SPACES L_p

摘要

We obtain upper estimates for the least upper bounds of approximations of the classes of Poisson integrals of functions from H_(ωp) for 1 ≤ p < ∞ by a certain linear method U~*_n in the metric of the space L_p.It is shown that the obtained estimates are asymptotically exact for p = 1. In addition, we determine the asymptotic equalities for the best approximations of the classes of Poisson integrals of functions from H_(ω1) in the metric of the space L_1 and show that, for these classes, the method U~*_n is the best polynomial approximation method in a sense of strong asymptotic behavior.